Quark Number Susceptibility in Deformed AdS

1. Quark Number Susceptibilityin Deformed AdS Kyung-il Kim December 10~11, 2010, Heavy Ion Meeting

2. Contents • Introduction • Quark number susceptibility • AdS/QCD at finite temperature • Hydrodynamics • AdS/CFT approaches to hydrodynamics • Deformed AdS space • Quark number susceptibility in AdS/QCD • Summary and Outlook 2010 Dec. 10~11 Heavy Ion Meeting 2/24

3. Quark Number Susceptibility Ref. Larry MclerranPRD 36 (1987) 3291 If the effective mass of baryons in the quark-gluon plasma is small compared to what it is in the hadron gas, then the baryon number concentrates in the region of quark-gluon plasma. The baryon number density near zero chemical potential In large N_c limit, 2010 Dec. 10~11 Heavy Ion Meeting 3/24

4. Quark Number Susceptibility Ref. Cheng et al. PRD 79, 074505 (2009) <The pressure> = Grand potential <The definition of susceptibility for various charge> Under conditions met in RHIC and LHC the net baryon number is small and QCD at vanishing chemical potential provides a good approximation. 2010 Dec. 10~11 Heavy Ion Meeting 4/24

5. Quark Number Susceptibility Lattice Results 2010 Dec. 10~11 Heavy Ion Meeting 5/24

6. AdS/QCD at finite temperature Geometry Confinement phase Thermal AdS Deconfinement phase AdS Black Hole The periodicity The Hawking temperature The black hole horizon The Euclidean gravitational action 2010 Dec. 10~11 Heavy Ion Meeting 6/24

7. Hydrodynamics The long-distance, low-frequency behavior of any interacting theory at finite temperature must be described by hydrodynamics. <The retarded thermal Green’s function> where, This function determines the response of the system on a small external source coupled to the current. When omega and q are small, the external perturbation varies slowly in space and time, and a macroscopic hydrodynamic description for its evolution is possible. 2010 Dec. 10~11 Heavy Ion Meeting 7/24

8. Hydrodynamics in AdS/QCD <The gravity/gauge theory duality> <The method to obtain the retarded Green’s function> i) From classical action, ii) With incoming-wave boundary condition at horizon, =1 at u=0 by definition of mode eq. iii) The retarded thermal Green’s function is 2010 Dec. 10~11 Heavy Ion Meeting 8/24

9. Hydrodynamics in AdS/QCD Ref. G.Policastro, D.T.Son and O.Starinets JHEP 09 (2002) 043 How do we calculate the retarded Green’s function in AdS? <The metric and action> <The equation of motion for gauge field> 2010 Dec. 10~11 Heavy Ion Meeting 9/24

10. Hydrodynamics in AdS/QCD <The Fourier decomposition> We choose, dimensionless quantities, The e.o.m can be written as, 2010 Dec. 10~11 Heavy Ion Meeting 10/24

11. Hydrodynamics in AdS/QCD The equation for time component We substitute, then, we obtain with incoming-wave condition, The equation for F(u) 2010 Dec. 10~11 Heavy Ion Meeting 11/24

12. Deformed AdS Space Ref. Y.Kim, T.Misumi, and I.j.Shin [arxiv 0911.3205] 5D action for scalar field Scalar field solution for Thermal AdS : AdS BH : σ=0 is assumed in AdS BH since this background corresponds to high temperature deconfined phase. 2010 Dec. 10~11 Heavy Ion Meeting 12/24

13. Deformed AdS Space The deformed AdS Black Hole <The back-reacted metric> where, <The Hawking temperature for black-hole> where, 2010 Dec. 10~11 Heavy Ion Meeting 13/24

14. Deformed AdS Space <Change of critical temperature by quark mass> If we consider only the effect of back-reacted quark mass, the changeof critical temperature is small. (Here the change of scale is not considered.) 2010 Dec. 10~11 Heavy Ion Meeting 14/24

15. Deformed AdS Space < A dimensionless coordinate> : u=1 is horizon and u=0 is boundary. The metric rewritten as where, 2010 Dec. 10~11 Heavy Ion Meeting 15/24

16. Quark Number Susceptibility <The 5D action for U(1) gauge field> with gauge choice, 5D gauge coupling constant The Fourier decomposition <The equation of motion for A_t> 2010 Dec. 10~11 Heavy Ion Meeting 16/24

17. Quark Number Susceptibility <The equation of motion for time component> We substitue, A solution as, 2010 Dec. 10~11 Heavy Ion Meeting 17/24

18. Quark Number Susceptibility The small parameter expansion of F(u) The solution is obtained as following, 2010 Dec. 10~11 Heavy Ion Meeting 18/24

19. Quark Number Susceptibility The solution of A_t <The quark susceptibility from the on-shell action> 2010 Dec. 10~11 Heavy Ion Meeting 19/24

20. Quark Number Susceptibility Thermodynamic analysis <The grand potential> The 5D bulk action on-shell action in Euclidean spacetime Solution of time-component of gauge field, when chemical potential is defined as, 2010 Dec. 10~11 Heavy Ion Meeting 20/24

21. Quark Number Susceptibility <The grand potential> <The quark number susceptibility> 2010 Dec. 10~11 Heavy Ion Meeting 21/24

22. Quark Number Susceptibility <The quark number susceptibility in deformed AdS> 2010 Dec. 10~11 Heavy Ion Meeting 22/24

23. Summary and Outlook • The quark number susceptibility has a feature that it is suppressed by quark mass. • Using hydrodynamic and thermodynamic approaches to AdS/QCD, we can obtain same result in quark number susceptibility. • Using D3/D7 model, in top-down approach we can obtain quark number susceptibility. 2010 Dec. 10~11 Heavy Ion Meeting 23/24

24. Thank you!